Question

Two trains start at the same time from two stations A and B proceeding towards B and A at 36 kmph and 42 kmph respectively. When they meet it was noticed that one train has moved 48 km more than the other. Find the distance between A and

• A. 468 km
• B. 672 km
• C. 624 km
• D. 684 km
• E. 486 km

Answer 1

The Correct Option is C

Step 1: Understand the problem.
Two trains start at the same time from stations A and B, moving towards each other. One train travels at 36 km/h and the other at 42 km/h. When they meet, it is noticed that one train has moved 48 km more than the other. We are asked to find the distance between stations A and B.

Step 2: Use the relative speed concept.
Let the distance between stations A and B be \( D \). The two trains meet after a certain time, and in that time, the relative speed of the two trains will be the sum of their individual speeds:
Relative speed = \( 36 + 42 = 78 \, \text{km/h} \)

Step 3: Let the time taken for the trains to meet be \( t \) hours.
In the time \( t \), the distance covered by the first train is \( 36 \times t \) and the distance covered by the second train is \( 42 \times t \). We are given that one train covers 48 km more than the other. Thus:
\( 42t - 36t = 48 \)
\( 6t = 48 \)
\( t = \frac{48}{6} = 8 \, \text{hours} \)

Step 4: Calculate the distance between A and B.
Now that we know the time \( t = 8 \) hours, we can calculate the distance between A and B using the relative speed:
Distance = Relative speed × Time
Distance = \( 78 \times 8 = 624 \, \text{km} \)

Step 5: Conclusion.
The distance between stations A and B is 624 km.

Final Answer:
The correct option is (C): 624 km.